In forestry, **quadratic mean diameter** or **QMD** is a measure of central tendency which is considered more appropriate than arithmetic mean for characterizing the group of trees which have been measured. For *n* trees, QMD is calculated using the quadratic mean formula:

where is the diameter at breast height of the *i ^{th}* tree. Compared to the arithmetic mean, QMD assigns greater weight to larger trees – QMD is always greater than or equal to arithmetic mean for a given set of trees. QMD can be used in timber cruises to estimate the standing volume of timber in a forest, because it has the practical advantage of being directly related to basal area, which in turn is directly related to volume.

^{[1]}QMD can also be calculated as:

where BA is stand basal area, n is the number of trees, and k is a constant based on measurement units - for BA in ft^{2} and DBH in inches, k=0.005454; for BA in m^{2} and DBH in cm, k=0.0000785.

## References

**^**Curtis, Robert O.; Marshall, David D. (2000), "Why quadratic mean diameter?" (PDF),*Western Journal of Applied Forestry*,**15**(3): 137–139, retrieved 2012-06-13